Big O in probability notation: Difference between revisions

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Equivalently, ''X''_''n'' = o_''p''(''a''_''n'') can be written as ''a''_''n'' o_''p''(1) where ''X''_''n'' = o_''p''(1) is defined as,

:<math>\lim_{n \to \infty} P(|X_n| \leqgeq \varepsilon) = 0,</math>

for every positive ε<ref>Yvonne M. Bishop, Stephen E. Fienberg, Paul W. Holland. (1975,2007) ''Discrete multivariate analysis'', Springer. ISBN 0387728058, ISBN 9780387728056</ref>.